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SUMMARY:Wei Rao
DTSTART:20261118T073000Z
DTEND:20261118T090000Z
DTSTAMP:20261109T050834Z
UID:Mos-Bei-top-seminar/171
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Mos-Bei-top-
 seminar/171/">Piercing theorems for discrete boxes</a>\nby Wei Rao as part
  of Moscow-Beijing topology seminar\n\n\nAbstract\nFor a finite family of 
 nonempty sets\, the piercing number \\tau is the minimum number of points 
 meeting every member\, while the packing number \\nu is the maximum size o
 f a pairwise disjoint subfamily. We will introduce classical and recent bo
 unds relating these parameters for axis-parallel boxes. We will then consi
 der discrete boxes\, obtained by intersecting boxes in R^d with a prescrib
 ed point set P. After briefly recalling general piercing results for discr
 ete boxes\, we will focus on the planar case and prove the bound \\tau = O
 (\\nu \\log \\nu)\, with a constant independent of P.\n
LOCATION:https://researchseminars.org/talk/Mos-Bei-top-seminar/171/
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